Question

Среднее арифметическое корней уравнения равно(х-0,5)(х+2)³+(0,5-х)(х-1)³=9х-4,5

Answer 1

(x-1/2)(x+2)^3-(1/2-x)(x-1)^3=9(x-1/2)
x1=1/2
(x+2)^3+(x-1)^3=9
(x+2+x-1)((x+2)^2+(x-1)^2-(x-1)(x+2))=9
(2x+1)(x^2+4x+4+x^2-2x+1-x^2-x+2)=9
(2x+1)(x^2+x+7)=9
2x^3+x^2+2x^2+x+14x+7=9
2x^3+3x^2+15x-2=0
x^3+3/2x^2+15/2x-1=0
x2+x3+x4=-3/2
x1+x2+x3+x4=1/2-3/2=-1
(x1+x2+x3+x4)/4=-1/4

Answer 2

(x-1/2)(x+2)^3-(1/2-x)(x-1)^3=9(x-1/2)
x1=1/2
(x+2)^3+(x-1)^3=9
(x+2+x-1)((x+2)^2+(x-1)^2-(x-1)(x+2))=9
(2x+1)(x^2+4x+4+x^2-2x+1-x^2-x+2)=9
(2x+1)(x^2+x+7)=9
2x^3+x^2+2x^2+x+14x+7=9
2x^3+3x^2+15x-2=0
x^3+3/2x^2+15/2x-1=0
x2+x3+x4=-3/2
x1+x2+x3+x4=1/2-3/2=-1
(x1+x2+x3+x4)/4=-1/4